ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician, English
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Mathematics
Areas: Algebra
Center Faculty of Mathematics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
Linear Algebra is an essential part of the mathematical toolkit required in the modern study of many areas of behavioral, natural, physical and social sciences, in engineering, in business, in computer science, and of course in pure and applied mathematics.
The purposes of this course is to develop the basic concepts of linear algebra and to illustrate their usability by means of a variety of selected applications. More precisely, one can say that the aims are:
i) To provide a first contact with algebraic structures: vector spaces and linear maps as a generalization of vectors in R^3 and matrices, respectively. To learn how to operate with vectors, basis, subspaces and linear maps.
ii)To get acquaintance with the use of matrices in different branches of knowledge.
iii) To understand the need for reducing matrices to predetermined forms and to practice the algorithms.
1.- Vector spaces. (5 theoretical hours)
Definition of vector space: Examples. Subspaces. Quotient spaces. Intersection and sum of subspaces. Systems of generators .
2.- Linear independence and dimension. (6 theoretical hours)
Linear dependence and independence. Bases and dimension. Equations for a subspace. Coordinates. Supplementary subspaces.
3.- Applications between vector spaces. (9 theoretical hours)
Definition of linear map: properties and examples. Subspaces associated to a linear map. The vector space of linear maps. Matrix of a linear map. Change of basis and linear maps.
4.- Matrices. (5 theoretical hours)
Operations with matrices and properties. Non singular matrices. Elementary matrices. Equivalent matrices. Rank of a matrix.
5.- Systems of linear equations. (3 theoretical hours)
Systems of linear equations. Gaussian elimination. The Rouché-Frobenius Theorem.
Basic.
1.-Cohn, P. M. Algebra, Vol. 1(2ª Ed.). Wiley and Sons, Chichester, 1982.
2.-Jeronimo, G., Sabia, J., Tesauri, S. Álgebra lineal. http://mate.dm.uba.ar/~jeronimo/algebra_lineal/AlgebraLineal.pdf.
3.-López Camino, Rafael. Apuntes Geometría I. Curso 2003-2004. Universidad de Granada.
https://www.ugr.es/~rcamino/docencia/geo1-03/g1tema1.pdf
https://www.ugr.es/~rcamino/docencia/geo1-03/g1tema2.pdf
https://www.ugr.es/~rcamino/docencia/geo1-03/g1tema3.pdf
4.-Notas para un curso de Álgebra Lineal. https://www.usc.es/regaca/apuntes/notas_alg_lin.pdf
Complementary
1.-Bolos, J.; Cayetano, J.; Requejo, B. Álgebra lineal y Geometría. UNEX, 2007.
2.-Merino, L.; Santos, E. Álgebra lineal con métodos elementales. Thomson, 2006.
Contribute to achieving the basic, general and transversal competences included in the report of the Degree in Mathematics of the USC: CB1, CB2, CB3, CB4, CB5, CG1, CG2, CG3, CG4, CG5, CT1, CT2, CT3, CT5.
Know the basic concepts of Linear Algebra.
Know the algorithms to reduce matrices to row-echelon forms and know how to apply them to the calculation of the range, calculation of base, resolution of systems, etc.
Understand the close relationship between matrices, linear applications and systems of linear equations and be able to use them in different contexts.
The Expository classes will be used for the presentation of the basic contents that compose this subject (CE1, CE2, CE6, CG1, CG4).
The interactive seminar classes in small groups, which will serve to illustrate the theoretical contents, will be dedicated to the resolution of questions and problems by the teacher with the participation of students (CB4, CT3, CE5, CE6).
In the interactive laboratory classes in very small groups, the questions and problems proposed will be worked on individually and / or in groups (CB2, CB3, CE3, CE4) and presentations will be made (CB4, CG4).
In the tutorials in the classroom in very small groups there will be a personalized follow-up of the learning of the students and of their work outside the class (CG5, CG4, CT5).
A course will be opened on the Virtual Campus in which there will be various support materials and activities scheduled (CT1, CT2, CT5, CG5).
Problem bulletins will be posted in the virtual course, programming them in a staggered way and always in relation to the theory.
Continuous assessment combined with a final test are planned as evaluation criterion. The final test will be held on the date set by the Faculty of Mathematics for that purpose.
Continuous assessment will consist of one test.
Calculation of the final qualification:
The final test, which will be compulsory, will be face-to-face. The qualification of both the first and the second chance will be the max {F; 0.3xC + 0.7xF} where C is the grade of the continuous assessment and F the grade of the final test.
The assessment system will be the same for the two groups of the subject.
For cases of fraudulent performance of exercises or tests, the provisions of the Regulations for the evaluation of students' academic performance and the review of qualifications will apply.
It will be considered as Not Presented that student that does not show to the final test, both in the first and in the second chance.
Expository classes:: 28
Seminar clases: 14
Laboratory clases: 14.
Tutorials in very small groups: 2
Personal work (non presential) of the student: 92
Total: 150
Study daily with the help of bibliographic material.
Carefully read the theoretical part until it is assimilated and try to answer the questions, exercises or problems presented in the bulletins.
Jose Manuel Fernandez Vilaboa
- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813167
- josemanuel.fernandez [at] usc.es
- Category
- Professor: University Professor
Rosa Mª Fernandez Rodriguez
Coordinador/a- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813158
- rosam.fernandez [at] usc.es
- Category
- Professor: University Lecturer
José Javier Majadas Soto
- Department
- Mathematics
- Area
- Algebra
- Phone
- 881813168
- j.majadas [at] usc.es
- Category
- Professor: University Professor
Brais Ramos Perez
- Department
- Mathematics
- Area
- Algebra
- braisramos.perez [at] usc.es
- Category
- USC Pre-doctoral Contract
Andres Perez Rodriguez
- Department
- Mathematics
- Area
- Algebra
- andresperez.rodriguez [at] usc.es
- Category
- Ministry Pre-doctoral Contract
| Monday | |||
|---|---|---|---|
| 10:00-11:00 | Grupo /CLE_01 | Galician, Spanish | Classroom 02 |
| 11:00-12:00 | Grupo /CLIL_06 | Galician, Spanish | Classroom 09 |
| 12:00-13:00 | Grupo /CLIL_05 | Spanish, Galician | Classroom 09 |
| 13:00-14:00 | Grupo /CLIL_04 | Spanish, Galician | Classroom 09 |
| Tuesday | |||
| 10:00-11:00 | Grupo /CLE_01 | Spanish, Galician | Classroom 02 |
| 12:00-13:00 | Grupo /CLIS_04 | Spanish | Classroom 08 |
| 13:00-14:00 | Grupo /CLIS_03 | Spanish | Classroom 09 |
| Wednesday | |||
| 13:00-14:00 | Grupo /CLE_02 | Spanish | Classroom 06 |
| Thursday | |||
| 09:00-10:00 | Grupo /CLIL_03 | Galician, Spanish | Classroom 08 |
| 10:00-11:00 | Grupo /CLIL_02 | Galician, Spanish | Classroom 08 |
| 11:00-12:00 | Grupo /CLIL_01 | Spanish, Galician | Classroom 08 |
| 12:00-13:00 | Grupo /CLE_02 | Spanish | Classroom 02 |
| Friday | |||
| 09:00-10:00 | Grupo /CLIS_01 | Galician, Spanish | Classroom 02 |
| 10:00-11:00 | Grupo /CLIS_02 | Galician, Spanish | Classroom 01 |
| 05.28.2024 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |
| 07.03.2024 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |